Skew-ed Up

Pj de Marigny, DITMo Strategies
Director, GARP S. California Chapter
“Skew-ed Up” (Ref: “Know Your Skew”)

Comments on “Know Your Skew” (Quest Partners, 07June2011, Research Paper)
Relating Skew to Range and other metrics

“Skew-ed Up”
28Sep2011, Newport Beach, CA. I liked the thought-provoking article on Skew/Range (“Know Your Skew,” Quest Partners, 07June2011, Research Paper, ) – and offer some comments. I would sum up the paper as follows:

Strategies that are Short VOL (long convergence) are more skewed. Using skew to determine range simply means that when out of normal conditions happen, Short VOL strategies will do increasingly worse. That doesn’t however, mean they are worse strategies.

The conclusion is: An investor has a choice of strategies that have better risk/return metrics at the expense of greater frequency of negative returns than implied by a normal distribution when conditions are abnormally bad; or, better consistency, lower skew or positive skew during abnormally bad conditions at the expense of worse risk/return metrics during normal conditions.

Absolute Return strategies (i.e. RV, Merger Arb, Event Arb, other derivative strategies) generally have negative skew. Momentum strategies generally are trend strategies that take on risk following a trend so the skew is low or positive. By the way, their summary statistics reflecting lower skew = better returns on abnormally bad market conditions includes SHORT SELLING strategies, that are the quintessential “LOW SKEW” strategies b/c they expect crappy returns always UNLESS there are abnormally bad market conditions prevail, therefore, relative to the mean (remember, skew is 3rd moment from the mean), they have more positive events when things go bad. What good is it to know that your range almost always is a negative return except in bad conditions?

The correct analysis would be to compare Abs Return strategies skew to the universe of only Abs Return strategies instead of comparing Abs Return strategies skew to momentum strategies. Momentum strategies and Short-selling will most always have lower skew. The report reflects the obvious: RV has lower sigma but greater “gamma” risk, or second derivative risk that underperforms momentum and short-selling strategies during abnormal (both directions) markets. Relative Value and Market Neutral strategies are capped upside, unlimited-downside-with-a-cushion-strategies that generally have better Sharpe, Lower VOL. Metrics of Max Drawdown (e.g. Sterling) to downside deviation or semi-variance (e.g. Sortino) are often used to evaluate and compare these strategies. Skew in and of itself, is meaningless, except to reflect that it indicates more observations in the negative tail than the normal distribution when conditions are abnormal. Standard Deviation reflects expected range of returns to a specified probability (normal market conditions) around the mean assuming a normal distribution.

Additionally, what the paper fails to distinguish in isolating Skew as an indicator to Return Range – is the magnitude of the asymmetry (i.e. Kurtosis). Skew alone doesn’t perceive scale so in relating this computation to Range in some metric is not intuitively clear. What causes the Max Drawdown (outlier negative returns) is not so much the “multitude” of observances in the left tail, but the “magnitude” of these observances, i.e., a Lepto-kurtotic attribution.

Even so, it is difficult to observe so-called “Black Swan” events in strategies subject to a “knock-in” feature that relies on parametric tests. Statisticians have attempted to overcome the “lack of observances” problems in discrete data series by creating proxy distributions (i.e. “Continuous” distributions) but the methodology still. Relating Skew to Correlation is like comparing average rainfall of the Sahara to the Mojave. Correlation not only fails to reflect scale, it is used in matrices to compare asset classes that are themselves correlated to changing underlying factors including psychological market factors (see Ray Dalio’s comments on correlation, Highbridge Capital).

The main graph in the paper is SKEW normalized to VOL. This is intrinsically incorrect from a statistician’s point of view. Scaling third moment to second moment is scaling to the same number: The deviation from the mean with a different exponent. The hypothesis drawn is based on the ratio of two derivatives of the same number that can lead to a spurious conclusion.

Almost all derivative strategies will have negative skew – what the article doesn’t specifically say is that derivatives have a lognormal distribution – overlayed on a normal distribution (on which skew is calculated) will appear skewed and lepto-kurtotic. Not to get to pointy-headed, in real life the option price (aka, “implied volatility”) doesn’t even follow the lognormal distribution away from the money – there’s a convexity or smile/smirk b/c derivative traders expect outliers more often than the distribution implies. Derivatives are leveraged by definition unless trading at their intrinsic value, as you know, and gamma increases as the derivative strike moves toward the money, then abates. For CTAs, they often use futures that are derivatives priced on basis spread less carrying costs, but no “theta.”

The difference between momentum players – like CTAs, Long/Short and Absolute Return players like Relative Value/Arb, Market Neutral – is captured in the Skew measurement that reflects the timing of when risk is layered on. Two of the lowest Skew strategies, SP500 and Short Selling, have neutral or positive skew, but Max Drawdown and Risk-Adjusted Returns suffer in comparison to all other strategies. Ranking strategies by using a ratio of SKEW-to-VOL results in punishing LOW-VOL Relative Value strategies. It is conceded that Sharpe should not be used to rank strategies and that this metric may be gamed in using derivatives. While there is no doubt that CTAs as an asset class has an alluring risk-adjusted return, the challenge is in comparison to the investable CTA index without taking on, as the article isolates, “tail risk” in offsetting the fees involved. A Hedge Strategy comparison monthly report is available FREE at: *.*

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